Hands-on Exercise 5.1

“In this hands-on exercise, I will learn to use using appropriate functions of spNetwork package: To derive network constrained kernel density estimation (NetKDE), and to perform network G-function and k-function analysis”

1. Overview

Network constrained Spatial Point Patterns Analysis (NetSPAA) is a collection of spatial point patterns analysis methods special developed for analysing spatial point event occurs on or alongside network. The spatial point event can be locations of traffic accident or childcare centre for example. The network, on the other hand can be a road network or river network.

In this hands-on exercise, I will learn using appropriate functions of spNetwork package:

• to derive network constrained kernel density estimation (NetKDE), and
• to perform network G-function and k-function analysis

2. Data

In this study, I will analyse the spatial distribution of childcare centre in Punggol planning area. For the purpose of this study, two geospatial data sets will be used. They are:

Punggol_St, a line features geospatial data which store the road network within Punggol Planning Area. pg_owin, a point feature geospatial data which store the location of childcare centres within Punggol Planning Area.

3. Installing and launching the R packages

In this hands-on exercise, four R packages will be used, they are:

spNetwork which provides functions to perform Spatial Point Patterns Analysis such as kernel density estimation (KDE) and K-function on network. It also can be used to build spatial matrices (‘listw’ objects like in ‘spdep’ package) to conduct any kind of traditional spatial analysis with spatial weights based on reticular distances.

rgdal which provides bindings to the ‘Geospatial’ Data Abstraction Library (GDAL) (>= 1.11.4) and access to projection/transformation operations from the PROJ library. In this exercise, rgdal will be used to import geospatial data in R and store as sp objects.

sp which provides classes and methods for dealing with spatial data in R. In this exercise, it will be used to manage SpatialPointsDataFrame and SpatiaLinesDataFrame, and for performing projection transformation.

tmap which provides functions for plotting cartographic quality static point patterns maps or interactive maps by using leaflet API.

packages = c('sp', 'rgdal', 'spNetwork', 'tmap')
for (p in packages){
if(!require(p, character.only = T)){
install.packages(p)
}
library(p,character.only = T)
}

4. Data Import and Preparation

The code chunk below uses readOGR() of rgdal package to important Punggol_St and Punggol_CC geospatial data sets as SpatialLinesDataFrame and SpatialPointsDataFrame respectively

network <- readOGR(dsn="data/geospatial", 
                   layer="Punggol_St",
                   verbose = FALSE)
childcare <- readOGR(dsn="data/geospatial",
                     layer="Punggol_CC",
                     verbose = FALSE)

Code chunk below can be used to print the content of network SpatialLineDataFrame and childcare SpatialPointsDataFrame.

Formal class 'SpatialLinesDataFrame' [package "sp"] with 4 slots
  ..@ data       :'data.frame': 2642 obs. of  2 variables:
  .. ..$ LINK_ID: chr [1:2642] "116130894" "116130897" "116130901" "116130902" ...
  .. ..$ ST_NAME: chr [1:2642] "PUNGGOL RD" "PONGGOL TWENTY-FOURTH AVE" "PONGGOL SEVENTEENTH AVE" "PONGGOL SEVENTEENTH AVE" ...
  ..@ lines      :List of 2642
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36547 36559 44575 44614
  .. .. .. ..@ ID   : chr "0"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36547 36491 44575 44589
  .. .. .. ..@ ID   : chr "1"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36013 36063 44154 44198
  .. .. .. ..@ ID   : chr "2"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36063 36087 44198 44214
  .. .. .. ..@ ID   : chr "3"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36132 36117 42756 42764
  .. .. .. ..@ ID   : chr "4"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36113 36117 42752 42764
  .. .. .. ..@ ID   : chr "5"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36127 36113 42745 42752
  .. .. .. ..@ ID   : chr "6"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 35995 35978 42428 42437
  .. .. .. ..@ ID   : chr "7"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 35985 35969 42407 42417
  .. .. .. ..@ ID   : chr "8"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36201 36216 42219 42241
  .. .. .. ..@ ID   : chr "9"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36242 36216 42220 42241
  .. .. .. ..@ ID   : chr "10"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:6, 1:2] 36344 36353 36362 36377 36394 ...
  .. .. .. ..@ ID   : chr "11"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:3, 1:2] 36344 36469 36491 44505 44493 ...
  .. .. .. ..@ ID   : chr "12"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36341 36344 44467 44505
  .. .. .. ..@ ID   : chr "13"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36063 36023 44198 44273
  .. .. .. ..@ ID   : chr "14"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 35955 36023 44233 44273
  .. .. .. ..@ ID   : chr "15"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36023 36056 44273 44294
  .. .. .. ..@ ID   : chr "16"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:3, 1:2] 35644 35651 35656 42586 42594 ...
  .. .. .. ..@ ID   : chr "17"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 35858 35846 42923 42929
  .. .. .. ..@ ID   : chr "18"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 35847 35835 42905 42912
  .. .. .. ..@ ID   : chr "19"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 35847 35858 42905 42923
  .. .. .. ..@ ID   : chr "20"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 35656 35671 42600 42623
  .. .. .. ..@ ID   : chr "21"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 35679 35656 42588 42600
  .. .. .. ..@ ID   : chr "22"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 35672 35644 42572 42586
  .. .. .. ..@ ID   : chr "23"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 35632 35644 42564 42586
  .. .. .. ..@ ID   : chr "24"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36100 36113 42725 42752
  .. .. .. ..@ ID   : chr "25"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36113 36090 42752 42767
  .. .. .. ..@ ID   : chr "26"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36090 36004 42767 42820
  .. .. .. ..@ ID   : chr "27"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36117 36088 42764 42781
  .. .. .. ..@ ID   : chr "28"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36117 36130 42764 42791
  .. .. .. ..@ ID   : chr "29"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36156 36127 42724 42745
  .. .. .. ..@ ID   : chr "30"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36112 36127 42710 42745
  .. .. .. ..@ ID   : chr "31"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36881 36859 42199 42215
  .. .. .. ..@ ID   : chr "32"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36859 36836 42215 42232
  .. .. .. ..@ ID   : chr "33"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36428 36401 42529 42548
  .. .. .. ..@ ID   : chr "34"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36456 36428 42508 42529
  .. .. .. ..@ ID   : chr "35"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36409 36428 42505 42529
  .. .. .. ..@ ID   : chr "36"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36847 36859 42199 42215
  .. .. .. ..@ ID   : chr "37"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:3, 1:2] 36412 36431 36449 42553 42554 ...
  .. .. .. ..@ ID   : chr "38"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:3, 1:2] 36460 36452 36449 42520 42538 ...
  .. .. .. ..@ ID   : chr "39"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:5, 1:2] 36409 36410 36409 36407 36401 ...
  .. .. .. ..@ ID   : chr "40"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:3, 1:2] 36849 36866 36882 42241 42243 ...
  .. .. .. ..@ ID   : chr "41"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:3, 1:2] 36889 36883 36882 42212 42227 ...
  .. .. .. ..@ ID   : chr "42"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:3, 1:2] 36847 36843 36836 42199 42215 ...
  .. .. .. ..@ ID   : chr "43"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
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  .. .. .. ..@ ID   : chr "44"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
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  .. .. .. ..@ ID   : chr "45"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36486 36499 41696 41714
  .. .. .. ..@ ID   : chr "46"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:5, 1:2] 36477 36482 36486 36487 36486 ...
  .. .. .. ..@ ID   : chr "47"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:4, 1:2] 36477 36471 36466 36464 41671 ...
  .. .. .. ..@ ID   : chr "48"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:5, 1:2] 36464 36466 36471 36478 36486 ...
  .. .. .. ..@ ID   : chr "49"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:3, 1:2] 35969 35973 35978 42417 42425 ...
  .. .. .. ..@ ID   : chr "50"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:3, 1:2] 35985 35989 35995 42407 42416 ...
  .. .. .. ..@ ID   : chr "51"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:3, 1:2] 36216 36222 36226 42241 42249 ...
  .. .. .. ..@ ID   : chr "52"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:3, 1:2] 36632 36636 36642 41902 41909 ...
  .. .. .. ..@ ID   : chr "53"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:3, 1:2] 36633 36636 36645 42816 42821 ...
  .. .. .. ..@ ID   : chr "54"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:3, 1:2] 37068 37072 37081 42504 42509 ...
  .. .. .. ..@ ID   : chr "55"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:6, 1:2] 36094 36105 36113 36115 36115 ...
  .. .. .. ..@ ID   : chr "56"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36094 36088 42065 42073
  .. .. .. ..@ ID   : chr "57"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:5, 1:2] 36088 36091 36096 36104 36112 ...
  .. .. .. ..@ ID   : chr "58"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36112 36135 42094 42129
  .. .. .. ..@ ID   : chr "59"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36135 36142 42129 42141
  .. .. .. ..@ ID   : chr "60"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36142 36173 42141 42178
  .. .. .. ..@ ID   : chr "61"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36173 36201 42178 42219
  .. .. .. ..@ ID   : chr "62"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36226 36206 42255 42271
  .. .. .. ..@ ID   : chr "63"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36251 36226 42235 42255
  .. .. .. ..@ ID   : chr "64"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36226 36244 42255 42281
  .. .. .. ..@ ID   : chr "65"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
  .. .. .. .. .. .. ..@ coords: num [1:2, 1:2] 36567 36588 41808 41840
  .. .. .. ..@ ID   : chr "66"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
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  .. .. .. ..@ ID   : chr "67"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
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  .. .. .. ..@ ID   : chr "68"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. .. .. ..@ ID   : chr "70"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
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  .. .. .. ..@ ID   : chr "71"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
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  .. .. .. ..@ ID   : chr "72"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. .. .. ..@ ID   : chr "73"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. .. .. ..@ ID   : chr "74"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
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  .. .. .. ..@ ID   : chr "78"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
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  .. .. .. ..@ ID   : chr "79"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
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  .. .. .. ..@ ID   : chr "80"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
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  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. .. .. ..@ ID   : chr "83"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. .. .. ..@ ID   : chr "84"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
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  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. .. .. ..@ ID   : chr "86"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. .. .. ..@ ID   : chr "88"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
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  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. .. .. ..@ ID   : chr "90"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
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  .. .. .. ..@ ID   : chr "92"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
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  .. .. .. ..@ ID   : chr "93"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
  .. .. .. .. ..$ :Formal class 'Line' [package "sp"] with 1 slot
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  .. .. .. ..@ ID   : chr "94"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
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  .. .. .. ..@ ID   : chr "95"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
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  .. .. .. ..@ ID   : chr "96"
  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
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  .. ..$ :Formal class 'Lines' [package "sp"] with 2 slots
  .. .. .. ..@ Lines:List of 1
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  .. .. .. .. .. .. ..@ coords: num [1:4, 1:2] 36261 36277 36287 36300 43036 ...
  .. .. .. ..@ ID   : chr "98"
  .. .. [list output truncated]
  ..@ bbox       : num [1:2, 1:2] 34039 40941 38883 44801
  .. ..- attr(*, "dimnames")=List of 2
  .. .. ..$ : chr [1:2] "x" "y"
  .. .. ..$ : chr [1:2] "min" "max"
  ..@ proj4string:Formal class 'CRS' [package "sp"] with 1 slot
  .. .. ..@ projargs: chr "+proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +to"| __truncated__
  .. .. ..$ comment: chr "PROJCRS[\"SVY21 / Singapore TM\",\n    BASEGEOGCRS[\"SVY21\",\n        DATUM[\"SVY21\",\n            ELLIPSOID["| __truncated__

Formal class 'SpatialPointsDataFrame' [package "sp"] with 5 slots
  ..@ data       :'data.frame': 61 obs. of  1 variable:
  .. ..$ Name: chr [1:61] "kml_10" "kml_99" "kml_100" "kml_101" ...
  ..@ coords.nrs : num(0) 
  ..@ coords     : num [1:61, 1:3] 36174 36480 36619 36285 35415 ...
  .. ..- attr(*, "dimnames")=List of 2
  .. .. ..$ : NULL
  .. .. ..$ : chr [1:3] "coords.x1" "coords.x2" "coords.x3"
  ..@ bbox       : num [1:3, 1:2] 34424 41504 0 37619 44686 ...
  .. ..- attr(*, "dimnames")=List of 2
  .. .. ..$ : chr [1:3] "coords.x1" "coords.x2" "coords.x3"
  .. .. ..$ : chr [1:2] "min" "max"
  ..@ proj4string:Formal class 'CRS' [package "sp"] with 1 slot
  .. .. ..@ projargs: chr "+proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +to"| __truncated__
  .. .. ..$ comment: chr "PROJCRS[\"SVY21 / Singapore TM\",\n    BASEGEOGCRS[\"SVY21\",\n        DATUM[\"SVY21\",\n            ELLIPSOID["| __truncated__

5. Assign CRS to OGR data

From the above results, we can see that the Projected CRS is SVY21. Hence, we can assign the EPSG code using the following code chunk:

childcare <-spTransform(childcare, CRS("+init=epsg:3414"))
network <- spTransform(network,CRS("+init=epsg:3414"))

6. Visualising the Geospatial Data

Before we jump into the analysis, it is a good practice to visualise the geospatial data.

There are at least two ways to visualise the geospatial data.

6.1 Using plot() of Base R as shown in the code chunk below

plot(network)
plot(childcare,add=T,col='red',pch = 19)

6.2 Using tmap package to visualise the geospatial data with high cartographic quality and interactive manner

tmap_mode('view')
tm_shape(childcare)+
  tm_dots() +
tm_shape(network)+
  tm_lines()

tmap_mode('plot')

7. Network Constrained KDE (NetKDE) Analysis

NetKDE analysis will be performed using appropriate functions provided in spNetwork package.

7.1 Preparing the lixels objects

• lixelize_lines() of spNetwork is used to cut SpatialLines object into lixels with a specified minimal distance
• Set length of a lixel, lx_length to 700m,
• Set minimum length of a lixel, mindist to 350m

lixels <- lixelize_lines(network,700,mindist = 350)
lixels

class       : SpatialLinesDataFrame 
features    : 2645 
extent      : 34038.56, 38882.85, 40941.11, 44801.27  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +units=m +no_defs 
variables   : 2
names       : oid.LINK_ID,   oid.ST_NAME 
min values  :  1032897752, EDGEDALE PLNS 
max values  :   998635154,      TRACK 24 

Other important notes:

• After cut, if length of final lixel is shorter than minimum distance, then it is added to previous lixel
• If NULL, then mindist = maxdist/10
• Segments that are already shorter than the minimum distance are not modified

7.2 Generating line centre points

lines_center() of spNetwork will be used to generate a SpatialPointsDataFrame (i.e. samples) with line centre points. The points are located at center of the line based on the length of the line.

samples <- lines_center(lixels)

8. Performing NetKDE

Code chunk below is used to compute the NetKDE

densities <- nkde(network, 
                  events = childcare,
                  w = rep(1,nrow(childcare)),
                  samples = samples,
                  kernel_name = "quartic",
                  bw = 300, 
                  div= "bw", 
                  method = "simple", 
                  digits = 1, 
                  tol = 1,
                  grid_shape = c(1,1), 
                  max_depth = 8,
                  agg = 5, #we aggregate events within a 5m radius (faster calculation)
                  sparse = TRUE,
                  verbose = FALSE)

More on the arguments:

• kernel_name indicates quartic kernel is used.
  • Other possible kernel methods supported by spNetwork are: triangle, gaussian, scaled gaussian, tricube, cosine, triweight, epanechnikov or uniform.
• method indicates simple method is used to calculate the NKDE. More on the possible methods supported by spNetwork:
  • simple: the distances between events and sampling points are replaced by network distances, and the formula of the kernel is adapted to calculate the density over a linear unit instead of an areal unit.
  • discontinuous: Equally “divides” the mass density of an event at intersections of lixels.
  • continuous: Divide the mass of the density at intersection but adjusts the density before the intersection to make the function continuous

9. Visualising NetKDE

9.1 Insert the computed density values (i.e. densities) into samples and lixels objects

samples$density <- densities
lixels$density <- densities

9.2 Rescale density values

Since svy21 projection system is in meter, the computed density values are very small i.e. 0.0000005. The code chunk below is used to resale the density values from number of events per meter to number of events per kilometer.

samples$density <- samples$density*1000
lixels$density <- lixels$density*1000

9.3 Plot map

The code below uses appropriate functions of tmap package to prepare interactive and high cartographic quality map visualisation.

tmap_mode('view')
tm_shape(lixels)+
  tm_lines(col="density")+
tm_shape(childcare)+
  tm_dots()

tmap_mode('plot')

We see from map above:

• Road segments with relatively higher density of childcare centres (darker color)
• Road segments with relatively lower density of childcare centres (lighter color)

10. Network Constrained G- and K-Function Analysis

• Here, we will perform complete spatial randomness (CSR) test by using kfunctions() of spNetwork package.

• The null hypothesis is defined as:

  • Ho: The observed spatial point events (i.e distribution of childcare centres) are UNIFORMLY DISTRIBUTED over a street network in Punggol Planning Area.

• The CSR test is based on the assumption of the binomial point process which implies the hypothesis that the childcare centres are randomly and independently distributed over the street network.

• If this hypothesis is rejected, we may infer that the distribution of childcare centres are spatially interacting and dependent on each other; as a result, they may form nonrandom patterns.

kfun_childcare <- kfunctions(network, 
                             childcare,
                             start = 0, 
                             end = 1000, 
                             step = 50, 
                             width = 50, 
                             nsim = 50, 
                             resolution = 50,
                             verbose = FALSE, 
                             conf_int = 0.05)

More on the arguments used above:

• lines: A SpatialLinesDataFrame with the sampling points. The geometries must be a SpatialLinesDataFrame (may crash if some geometries are invalid).
• points: A SpatialPointsDataFrame representing the points on the network. These points will be snapped on the network.
• start: A double, the start value for evaluating the k and g functions.
• end: A double, the last value for evaluating the k and g functions.
• step: A double, the jump between two evaluations of the k and g function.
• width: The width of each donut for the g-function.
• nsim: An integer indicating the number of Monte Carlo simulations required. In the above example, 50 simulation was performed. Note: most of the time, more simulations are required for inference
• resolution: When simulating random points on the network, selecting a resolution will reduce greatly the calculation time. When resolution is null the random points can occur everywhere on the graph. If a value is specified, the edges are split according to this value and the random points are selected vertices on the new network.
• conf_int: A double indicating the width confidence interval (default = 0.05)

The output of kfunctions() is a list with the following values:

• plotkA, a ggplot2 object representing the values of the k-function
• plotgA, a ggplot2 object representing the values of the g-function
• valuesA, a DataFrame with the values used to build the plots

10.1 Visualise the ggplot2 object of k-function

kfun_childcare$plotk

From the plot above:

• blue line is the empirical network K-function of the childcare centres in Punggol planning area

• gray envelop represents the results of the 50 simulations in the interval 2.5% - 97.5%

• Because blue line between the distance of 250m-400m are below the gray area, we can infer that the childcare centres in Punggol planning area resemble regular pattern at the distance of 250m-400m.

10.2 Visualise the values object of k-function

kfun_childcare$values

         obs_k    lower_k    upper_k      obs_g    lower_g   upper_g
1      0.00000     0.0000     0.0000    0.00000    0.00000  289.3310
2      0.00000     0.0000   433.9966   72.33276   16.27487  417.7217
3     72.33276   144.6655   707.0527    0.00000   16.27487  618.4451
4     72.33276   289.3310  1269.4399   72.33276   16.27487  578.6621
5    361.66380   506.3293  1663.6535  289.33104   72.33276  779.3855
6    650.99483   811.9352  2433.9973  216.99828  233.27315  891.5013
7    795.66035  1229.6569  2867.9939  289.33104  233.27315  940.3259
8   1229.65691  1824.5939  3848.1028  578.66207  289.33104 1285.7148
9   2097.65002  2491.8636  5045.2100 1084.99139  433.99656 1414.1054
10  3182.64140  3327.3069  6122.9681 1084.99139  506.32931 1486.4382
11  4195.30003  4195.3000  7016.2776  650.99483  594.93694 1719.7114
12  4773.96211  5072.3347  8622.0649 1301.98967  795.66035 1808.3190
13  6654.61385  5867.9951 10461.1253 2097.65002  723.32759 2193.4909
14  8390.60007  6985.5362 11916.8221 1663.65346  611.21182 1952.9845
15 10054.25353  7990.9616 13893.3147 1591.32070  828.21009 2153.7079
16 12079.57079  9171.7939 15896.9322 1808.31898  940.32587 2603.9793
17 14032.55528 10632.9156 18050.6401 2097.65002  916.81772 2643.7623
18 16202.53806 11750.4567 20179.0315 2603.97933 1245.93178 2748.6448
19 18661.85187 13453.8932 21996.3921 2459.31381 1117.54113 3141.0501
20 21338.16396 14972.8812 24311.0404 2676.31209 1045.20837 3021.7010
21 24014.47605 16251.3627 27066.9185 2712.47847 1479.20493 3294.7572
   distances
1          0
2         50
3        100
4        150
5        200
6        250
7        300
8        350
9        400
10       450
11       500
12       550
13       600
14       650
15       700
16       750
17       800
18       850
19       900
20       950
21      1000